Omphalos and Snake: Shared Iconography

I’m really stuck on this Alföldi article. [See yesterday’s post for references.] He makes the assertion that the snake on an omphalos is the iconography of Apollo, not Aesculapius. He uses Etruscan cinerary urns as comparative evidence:

Yet these visual examples do not specifically link the image to Apollo they only show Italic usage. The image is clearly Delphic as Alföldi asserts. A point illustrated by the late 4th century Amphictonic Hemidrachms:

But this is by no means exclusive. The same reverse type was used at Pergamon after 133 BC to celebrate Aesculapius as Soter (savior):

Aesculapius has been a popular interpretation of the allusions on L. Rubrius Dossenus’ coins because of literary testimony of a plague in 87 BC. However, if Apollo is meant than these coins might be linked to the Veiovis / Apollo coins of the Marians. The interpretation of which remains controversial: